Orthogonal Frequency Division Multiplexing (OFDM) is a widely known modulation scheme in which a digital serial data bit stream is split into parallel data bit streams that each modulate a different carrier, known as subcarrier, of a group of orthogonal carriers. The subcarriers are spaced apart at precise frequencies which prevents a receiving demodulator from distortions by frequencies other than the subcarrier frequency to which the demodulator is allocated. The bit rate of each parallel data stream is a fraction of the bit rate of the serial data bit stream, dependent on the number of subcarriers. Each subcarrier is modulated by a conventional modulation scheme, such as Quadrature Amplitude Modulation (QAM) and Quadrature Phase Shift Keying (QPSK), providing so-called OFDM symbols at a low symbol rate, i.e. where the symbols are relatively long compared to the channel time characteristics. An OFDM symbol comprises a number of data bits dependent on the modulation scheme used. The modulated subcarriers are combined together using an Inverse Fast Fourier Transform (IFFT) to yield a time-domain waveform to be transmitted. The total bit rate of all the subcarriers is comparable to a conventional single-carrier high-rate modulation scheme in the same bandwidth.
Since the duration of each symbol is relatively long, it is feasible to insert a guard interval between the OFDM symbols, also referred to as Cyclic Prefix (CP), for eliminating inter-symbol interference. However, the increased symbol duration makes an OFDM system more sensitive to the time variations of mobile radio channels. In particular, the effect of Doppler spreading destroys the orthogonality of the subcarriers, causing Inter-Carrier Interference (ICI), i.e. cross-talk between the sub-carriers. OFDM requires also a very accurate frequency synchronization between a receiver and transmitter.
In an OFDM like system, e.g. Long Term Evolution (LTE) or Evolved Universal Terrestrial Radio Access (E-UTRA), which is currently under development with the 3rd Generation Partnership Project (3GPP) and disclosed in Technical Specification 3GPP TS 36.211 (Release 8), downlink radio transmission from a Base Station (BS) to User Equipment (UE) or Mobile Station (MS) is based on OFDM. The symbol information is related to the frequency bins (sub-carriers) of a Fast Fourier Transform (FFT). In the event that the carrier frequency at a BS and UE differs, a so-called frequency offset error occurs. In principle, the error is manifested as a shift of the subcarriers. The consequence is leakage, where spectral content from a user is spread to all users. To overcome this a user must be compensated for the frequency offset. In order to carry out the compensation the frequency error must be known. To his end a frequency estimator is used. The uplink, i.e. radio transmission from the MS to the UE, is based on SC-FDMA (Single Carrier-Frequency Division Multiplexing), which can be seen as a pre-coded version of OFDM.
A common method to estimate frequency offset is to use known signals, i.e. reference or pilot signals. These reference signals are transmitted regularly which means that the same signal will occur at over and over again. Exploiting a received reference signal provides an estimate of the frequency error. Several algorithms for frequency estimation are known in practice.
By way of example, in LTE a large number of narrow subcarriers is used for multi-carrier transmission. The basic LTE downlink resource is a time-frequency grid comprised of OFDM symbols, also called resource elements. In the frequency domain a resource element has a frequency bin of 15 kHz, which is the frequency spacing, Δf, between adjacent subcarriers. In the time domain the duration of an OFDM symbol or resource element is (1/Δf)+CP. The resource elements are grouped into resource blocks. A resource block has a total size of 180 kHz in the frequency domain, i.e. twelve resource elements, and 0.5 ms in the time domain, i.e. seven resource elements, called a time slot.
Resource blocks are transmitted in a so-called Transmission Time Interval (TTI) consisting of two time slots. Each user is allocated a number of resource blocks in the time-frequency grid. Which resource blocks and how many a user gets at a given point in time depends on advanced scheduling mechanisms, defined to enable optimal performance for different services in different radio environments.
In LTE uplink, per TTI two reference signals in the time domain are transmitted. This means that the distance between two similar reference signals or pilots is 0.5 ms. This fact limits the usable range for estimating frequency errors to the interval ±1000 Hz. In principle the range follows from the sampling theorem which states that the sampling frequency must be at least twice the highest frequency of the sampled signal. The time separation between two pilot signals is 0.5 ms which correspond to a sampling frequency of 2000 Hz. Evidently, it is possible to, unambiguously, resolve frequencies up to 1000 Hz.
According to the 3GPP standard, 3rd Generation Partnership Project, Technical Specification Group Radio Access Network; 25.913 v7.0.0 edition, 2005.a user should be able to travel at a speed of 350 km/h and the BS should be accurate to ±0.1 part per million (ppm) of the RF carrier frequency. This implies that if the RF carrier frequency is 2.5 GHz and including additional clock errors of 200 Hz, the frequency offset estimation must be able to resolve frequencies in a range up to ±1800 Hz. Hence, a frequency estimator using the information in two consecutive repetitive received reference signals in the time domain cannot meet the desired range.
In the frequency domain in LTE, using the reference symbols of a single reference signal for frequency error estimation, the usable range is limited to the interval ±15 kHz, i.e. the frequency spacing Δf between reference symbols of adjacent subcarriers onto which the reference signal is modulated. This range is too coarse for meeting the desired range.